Probability hypothesis density filter with uncertainty in the probability of detection

Abstract

The space around the earth is becoming increasingly populated. Efficient tracking algorithms are hence integral to protect active space assets from collisions. Ground-based measurements are the primary source of information for any tracking algorithm. Multi-Target Tracking (MTT) algorithms use the measurements to jointly estimate the number of objects and their states in a surveillance scene. MTT has mainly been developed by two approaches: the track-based approach and the population-based approach. Population-based approaches are formulated using Finite Set Statistics (FISST) and have been widely researched in the past decade. A critical component of the population-based algorithms is the probability of detection (pD), which determines how likely it is that a measurement can be obtained from an object. pD is usually modeled as a constant quantity, when it is exactly known. This assumption is not valid in the space environment, where pD depends on the state of the object, the object’s attitude and the materials used to make it. Such information is often vague or unknown for space objects. This research focuses on designing a pD model that takes into account the state dependency of pD and, most importantly, the uncertainty in pD. The MTT algorithm considered in this work is the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter. A variation of GM-PHD filter that incorporates the uncertainty and the state dependency of pD is developed and validated in this work. Results are validated via simulations of an orbital tracking scenario.